Superhedging and Dynamic Risk Measures under Volatility Uncertainty

Superhedging and Dynamic Risk Measures under Volatility Uncertainty

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strategy is obtained from a representation similar to the optional decomposition. F...

G–Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty

Risk Measures in Engineering Design under Uncertainty

Engineering decisions are invariably made under substantial uncertainty about current and future system cost and response, including cost and response associated with low-probability, high-consequence events. A risk-neutral decision maker would rely on expected values when comparing designs, while a riskaverse decision maker might adopt nonlinear utility functions or failure probability criteri...

Optimal Derivatives Design under Dynamic Risk Measures

We develop a methodology to optimally design a financial issue to hedge non-tradable risk on financial markets. Economic agents assess their risk using monetary risk measure. The inf-convolution of convex risk measures is the key transformation in solving this optimization problem. When agents’ risk measures only differ from a risk aversion coefficient, the optimal risk transfer is amazingly eq...

Robust Optimal Stopping under Volatility Uncertainty

We study a robust optimal stopping problem with respect to a set P of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from P. We show that the upper Snell envelope Z of the reward process Y is a supermartin...